Cochran-Mantel-Haenszel

Conditional independence of a dichotomous categorical outcome

The Cochran-Mantel-Haenszel test is used to assess "conditional" independence of categorical predictors associated with categorical outcomes. This means that independent groups will differ in the association with a dichotomous categorical outcome across various "conditions" that the association is thought to exist within concurrently. The Cochran-Mantel-Haenszel test is an extension of the Chi-square test where the bivariate association between two dichotomous categorical variables is assessed in different treatment "conditions." The test yields a primary p-value testing for the meeting of conditional independence as well as an odds ratio with 95% confidence interval associated with the main effect.

The figure below depicts the use of a Cochran-Mantel-Haenszel test. There are independent groups being compared on a dichotomous categorical outcome, within the context of different conditions.

The steps for conducting a Cochran-Mantel-Haenszel test in SPSS

1. The data is entered in a between-subjects fashion.

2. Click Analyze.

3. Drag the cursor over the Descriptive Statistics drop-down menu.

4. Click on Crosstabs.

5. Click on the "grouping" variable or categorical predictor variable to highlight it.

9. Click on the categorical variable that denotes the different values or "levels" of the condition that is being tested.

10. Click on the arrow in the Layer 1 of 1 table to move the condition variable into the box.

11. Click on the Statistics button.

12. Click on the Cochran's and Mantel-Haenszel statistics box to select it.

13. Click Continue.

14. Click OK.

The steps for interpreting the SPSS output for a Cochran-Mantel-Haenszel

1. The Crosstabulation shows the frequency statistics associated with the analysis.

2. In the Tests of Homogeneity of the Odds Ratio table, look under the Asymp. Sig. (2-sided) column. If the p-values are ABOVE .05, then continue with the analysis. If the values are BELOW .05, then researchers have violated this statistical assumption and should run separate bivariate analyses.

3. If researchers met the assumption above, then look in the Tests of Conditional Independence table under the Asymp. Sig. (2-sided) column.

If the p-values are BELOW .05, then researcheres have evidence of conditional independence between the groups on the outcome. This means that the association between the predictor and outcome variable is significantly different in the different levels of the conditional variable.

If the p-values are ABOVE .05, then researchers do not have evidence of conditional independence between the groups. This means that the groups do not differ in their relationships with the outcome variable according to what condition they are in.

﻿Click on the Download Database and Download Data Dictionary buttons for a configured database and data dictionary for Cochran-Mantel-Haenszel.Click on the Validation of Statistical Findings button to learn more about bootstrap, split-group, and jack-knife validation methods.

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